ALGEBRAIC COBORDISM AND GROTHENDIECK GROUPS OVER SINGULAR SCHEMES

作者：Dai Shouxin^*

来源：Homology, Homotopy and Applications, 2010, 12(1): 93-110.

• algebraic cobordism
• Grothendieck groups
• singular schemes

A theorem of Levine-Morel states that algebraic cobordism groups are isomorphic to (multiplicative) Grothendieck groups over smooth schemes. We extend this theorem to singular schemes. As a consequence, we provide a new proof of the singular Riemann-Roch theorem of Baum-Fulton-MacPherson and a new type of Riemann-Roch theorem with respect to pullbacks of locally complete morphisms.

• 出版日期2010